Shear-free geodesics [1]} with \(\theta =\theta _0\) , are possible when \(P_\theta =0\)  i.e.
\(K^2_{s-free} = {J_\phi ^2 \over \sin ^2\theta _0} + {J_\psi ^2 \over \cos ^2\theta _0} + a_f^2E^2\sin ^2\theta _0\) 
